- With Special Thanks to Kenneth and Roswell Miller, Creators of the APBA Computer Baseball Game.


Below are definitions of terms used by StatMaster with which you may not

be familiar.


In certain cases we have identified the person who introduced the concept

as it is used today. In a few cases the definition given differs

slightly from the definition used by its creator to account for statistics

that are not kept by APBA BASEBALL.


Where possible, we give ranges and average values of each performance measure

for teams or players in the big leagues.


Defensive Efficiency Record (DER)-- A measure of what percentage of balls

put into play against a team were converted to outs.  A Bill James



DER is calculated by dividing Plays Made (PM) by the sum of Plays Made

and Plays Not Made:


     DER = PM/(PM+OH-OHR+(.71)E)


("O" in front of a stat means "opposition"; .71E is an estimate of the

number of team errors which allowed a batter to get on base.)


Plays Made--or the number of balls put into play which were turned into

outs--is calculated by taking the average of two estimates.


     Est. #1    PM = PO-OSO-OCS-A(of)-.93TG


Explanation: a ball put into play is an out if it's a putout unless it's

a strikeout, or a caught stealing, or a runner put out on the bases, or

if more than one out was made on the play (.93 is an approximation of

the average number of double plays, plus two times triple plays made by

each major-league team in a game.)


     Est. #2    PM = OAB+OS-OH-OSO-(.71)E


Explanation: a ball put into play is an out if it's an opposition at bat

or a sacrifice bunt/fly unless it's a hit, or a strikeout, or a batter who

was allowed to reach base on an error.


Bigs: an average DER for major-league teams is about .695, which is to

say that about 3 balls in 10 that were put into play were hits or led

to errors, and about 7 in 10 were converted to outs.


Earned Runs Prevented -- The "Linear Weight" measure of a pitcher's

performance. (See also Runs Contributed.) A measure of how many runs

a pitcher prevented compared to an average pitcher in the league who

pitched the same number of innings.  (Earned runs prevented may be

translated into losses prevented by dividing by runs required per win

for that league.)  Remember that ERP measures the extent to which

a pitcher is better than average, not his total contribution.


Runs-prevented leaders are published weekly in the New York Times

(currently on Wednesdays) and in other newspapers.  A Pete Palmer



Earned runs prevented = (ERA - league ERA)/(IP/9)


Bigs: best ERP = 30 to 60 runs per 162-game season (30-40 starts).

Average ERP = 0.


Fielding Percentage -- The percentage of balls handled that were fielded

cleanly.  PCT = (PO+A)/(PO+A+E)


Bigs: average performance differs by position.  A typical season might

be P--.958, C--.986, 1B--.992, 2B--.981, 3B--.955, SS--.963, and OF--.981.


Modern major-league teams generally field from .970 to .985 overall;

leagues average .979.  Note: in BASEBALL 1.0, there were too many outfield

errors.  BASEBALL 1.1 corrected that.


The differences between team fielding percentages is about 1.5% and between

individual players (non-pitchers), no more than 3-4% at each position.


These are indicators--along with URP below--that fielding is not a major

factor in run prevention/creation, not when compared to pitching and

batting.  Sabermetric analysis, as practiced by Messrs. Palmer, Thorn,

and others, concludes that fielding is about 6% of baseball, pitching 44%,

and batting 50%.  Every player, manager, and fan, of course, has an

opinion about the relative importance of various aspects of the game.


We suspect that, happily, disagreements about methods of baseball analysis

will persist.


Offensive Support -- The average number of runs that a team scored in

games started by an individual pitcher.  A measure of how much better or

worse a pitcher is than his won-lost record indicates.  Pitchers with less

than average support may have been better than their record indicates, and

pitchers with more than average support may have been worse.


Bigs: most support = 5.5 to 6.5 runs per game; least support = 2.9 to 3.5

runs per game.  Average support is just the average runs scored by each

team in a game: in 1986, 4.18 r/g without the DH, 4.61 r/g with the DH,

and 4.41 r/g overall.


On-base Percentage (OBP) -- A measure of how often a batter reaches base due

to his effort as a percentage of his opportunities to reach.


      OBP = (H+BB+HP)/(AB+BB+HP)


Bigs: typically, league OBP = .330, team OBP = .300 to .340, player

OBP = .250 to .450.


Opposition Batting Average (OBA) -- The batting average of the opponents of a

specific team or pitcher against that team or pitcher.


      OBA = OH/OAB


For individual pitchers, an approximation is used: OBA = OH/((IP*3)+OH).

The actual OBA would be 10 to 14 points higher after adjusting for outs

made on the base paths by players whose plate appearance was not an at bat.


Bigs: league OBA = league batting average (recently has been approximately

.255 without DH, .265 with DH), team OBA = same as team batting averages

(typically .230 to .280), pitcher OBA = .200 to .300.


Opposition Stolen Base Average (OSBA) -- The average number of opposition

stolen bases per game in games started by each catcher or pitcher.


A measure of their effectiveness at stopping the running game.  A Bill James



      For catchers: OSBA = (OSB/GS at catcher).

      For pitchers: OSBA = (OSB/GS).


Bigs: for catchers and pitchers, about .5 to 1.3 stolen bases allowed per

game (less is better).


Opposition Stolen Base Percentage (OSBP) -- See Stolen Base Percentage.


Power Average -- A player's slugging average minus his batting average.

Bill James calls this Isolated Power.  Branch Rickey championed this stat.


Power average is a measure of a player's ability to hit for power

considered apart from his ability to hit singles.


       PA = Slg - BA


Bigs: in 1986, league PA = .127 without DH; .146 with DH.  Team PA = .091

to .147 without DH; .130 to .167 with DH.  For an individual, PA under .080

means he can be considered a singles hitter; PA over .200 is very good power.


Quality Starts (QS) -- The number of starts in which a pitcher went at least

six innings and yielded no more than three earned runs.


Bigs: quality starts in over 60% of games started is considered good.


Range Factor -- The number of chances accepted per game.  A Bill James



      Range = (PO+A)/DG


Bigs: performance differs by position.  Typical season range factors might

be 2B--4.50 to 6.00, 3B--2.00 to 3.30, SS--4.00 to 5.30, R/LF--1.50 to 2.50,

and CF--2.30 to 3.20.  BASEBALL 1.0 skewed slightly the outfielder range factors.

APBA BASEBALL 1.1 corrected that. See the note under Fielding



Runs Contributed -- An estimate of the number of runs contributed to

a team's offense by each player above the number contributed by an average

player in the league.


Like runs created, runs contributed is an attempt to measure the overall

offensive contribution of a player in terms of the only thing that

ultimately counts, number of runs.  If you divide runs contributed by the

runs required per win (approximately 10, see "Runs Required Per Win"),

you have the wins contributed by this player's offensive performance above

the league average.  A Pete Palmer statistic.


Pete actually calls runs contributed "Batting Runs" to distinguish it from

Defensive Runs, Stolen Base Runs, and Pitching Runs, all "Linear Weights,"

and all measures of contributions to the team stated in terms of runs. (For

Pitching Runs, see "Earned Runs Prevented.") 


In the formula below, we use the historical average .25 for the league factor

(it can vary from approximately .24 to .26 from one year to the next).


This means that the sum of runs contributed for all players is not precisely zero,

as it would be if the league factor were adjusted to overall league performance.


In comparing players from a single season, their relative performance is

not changed by using this approximation.


      Runs contributed = (.46)S+(.80)D+(1.02)T+(1.40)HR+(.33)(BB+HP)



Bigs: an average player would contribute approximately zero (0) runs above

average.  An average outfielder might contribute 20 runs in 400 plate

appearances above the average player in the league.


On the other hand,a good shortstop might be expected to contribute no runs above

the average player in the league.  Clearly, outfielders are expected to be better

offensively than shortstops.


Players having great seasons contribute 40 to 70 runs; very poor seasons

are in the range -40 to -20.  Only players who play a lot can have a very

high or low season total, since the absolute number is dependent on number

of games played.


Runs Created -- An estimate of the number of runs that a player would

produce based on his offensive statistics. Runs created is an attempt to

measure total offensive contribution in terms of runs (see also Runs

Contributed).  Divided by the runs required per win (in professional

baseball, approximately 10), runs created becomes the total wins created

by this player's offensive performance. A Bill James statistic.


      RC = ((H+BB+HBP-CS)*(TB+.26(BB+HBP)+.52(SB+SAC)))/(AB+BB+HBP+SAC)


If a player is used primarily as a pinchrunner with few plate appearances

(CS > (H+BB+HBP)), then a different formula is used to try and capture the

players contribution. The (((H+BB)*TB)/(AB+BB)) part of the formula is the

basic runs created formula.


      RC = ((.52*SB)-CS) + (((H+BB)*TB)/(AB+BB))


Bigs: typically ranges from 0 to 120 in a 162-game season, more than 40 for

the best starting players.  Only players who play a lot can have a very high

season total, since the number is dependent on total stats.  For a team, runs

created is a projected estimate of the runs the team should have scored given

its number of hits (by type), walks, stolen bases, and times caught stealing.

Comparing team runs created to actual runs scored gives an indication of other

factors at work, factors that effect the efficiency of a team's offense.


For instance, high efficiency -- consistently scoring more runs than projected --

could be explained by good clutch hitting, good baserunning, good managing, or

good luck. The more consistent the two figures, the less luck is probably involved.


Runs Required Per Win -- A measure of the number of runs that are

required to win one more game.  This is not the number of runs that are

needed to win any single game, but rather the number that when added to

total team runs, would project to one more win for the team.


Historically for professional baseball it has been approximately 10, varying from

year to year between 9 and 11.


In APBA leagues in which the talents of players are not representative of baseball

as a whole -- many small leagues will have very good pitching or hitting -- the

runs required per win may vary more widely.  It is important to take this into

account when you are evaluating the runs created and runs contributed of an

individual player, especially when you are comparing performances from one year

to another.


In your league, suppose it takes 9 runs one year to create a win, and because of

great hitting in the league, it takes 12 runs the next year.  A player who

contributes 36 runs in the first year will have contributed 4 wins more than the

average player, while this same performance will only be 3 wins above average the

next year.  See Pete Palmer.


      Runs required per win = sq rt (league runs/(league innings pitched/2))*10


Slugging Percentage (SLG) -- A measure of a hitter's power and batting average combined. 


      Slg = TB/AB


Bigs: in general league Slg = .380 without DH, .408 with DH (1986 stats,

up from .376 and .401 in 1983).  Team Slg = .325 to .450, player Slg = .250 to .500.


Stolen Base Percentage -- The success rate of stealing bases.


Sabermetricians appear to be in wide agreement that if an individual's

or a team's base stealing percentage is less than .670 (67% or 2 out of 3

successful), then the running game is costing the team more runs than it

is creating. 


      SB Pct = SB/(SB+CS)


Bigs: in recent years the annual stealing success rate has been between .630

and .710 for professional baseball divisions, between .550 and .770 for teams,

and varies widely for individuals.  A league-leading percentage among frequent

base stealers is generally around .800 (80% successful).


For a team, 1.4 attempts/game is a lot; .6 attempts/game is very few.


In 1986 professional baseball players stole successfully at a rate of .672, so

their base stealing contributed approximately nothing to overall run production.

A Project Scoresheet study by Kevin Hoare provides strong evidence that base

stealing attempts lower the batting average of the player at bat during the

attempt, possibly by as much as 50 batting average points and 100 slugging average



Stealing attempts also increase on-base average, possibly by 40 points or more, but

this does not appear to outweigh the negative impact on batting.  More research is

called for in this area.  In APBA BASEBALL, stealing attempts reduce the batting

average of the player at bat.


Total Average -- A ratio of the bases a player accumulates for his team and the outs

he costs his team.  Total average is a Thomas Boswell statistic included in a

delightful book, "How Life Imitates the World Series."


      Total average = (TB+BB+SB+HP-CS)/(AB-H+CS)


APBA DOS BASEBALL does not count double plays, so players who hit into many DPs

will appear better in total average than they would if the complete TA formula

were used.  Using the above formula, division total averages for 1986 were .682

and .667 without the DH and .729 and .694 with the DH.


If a player has a TA over 1.000, that's very good.


Total Bases -- The total number of bases achieved by the batter on hits.

As with most stats, to make total bases indicative, it must be put in the

context in which it occurred.  For instance, total bases divided by at bats

is slugging percentage, which is one indicator of power.


      TB = S+(2*D)+(3*T)+(4*HR)


Bigs: in 1986 teams without the DH averaged 12.9 total bases/game; with

the DH, 13.9 total bases/game.


Total Plate Appearances -- The number of times a player appeared as

a batter.  TPA is sometimes used as the context for evaluating another

counter stat or as a condition for qualifying for the leader boards (see

Offensive Leader Boards). 


      TPA = AB+BB+HB+S


Bigs: teams averaged 38.2 plate appearances/game in 1986.


Unearned Run Percentage (URP) -- Unearned runs allowed by a team as a

percentage of total runs allowed. 


      URP = (R-ER)/R


Bigs: overall, for professional baseball in 1986, URP = .106, that is,

about 10% of the runs were unearned.  Teams' URP varied from .077 to .129.

See Fielding Percentage discussion above.


PA. Plate Appearances. A plate appearance occurs every time a batter steps up

to the plate. In other words, a player is credited with a plate appearance

every time he makes an out, reaches base via a hit, walk or an error, or hits

a sacrifice bunt or sacrifice fly.


PA/HR. Plate appearances per homerun. This tells you how many times on average

that a player comes to the plate before he can be expected to hit a homerun.


PA/RB. Plate appearances per successful reaching of base. The average number of

plate appearances before a batter gets on base, either through a walk, HBP, or a

base hit. For DOSBall purposes, this does NOT include the times that a batter

reached via an error.


PA/BB. Plate appearances per walk. The number of plate appearances it takes for a

particular player to reach base via a base on balls.


PA/K. Plate appearances per strikeout. The number of plate appearances it takes

for a particular player to strikeout.


PA/H. Plate appearances per hit. The number of plate appearances it takes for a

particular player to get a hit.


PA/R. Plate appearances per run. The number of plate appearances it takes for a

particular player to score a run.


PA/XBH. Plate appearances per extra base hit. The number of plate appearances it

takes for a particular player to get a double, triple or a homerun.


PA/HBP. Plate appearances per hit by pitch. The number of plate appearances it takes

for a particular player to reach base via hit by pitch.


XBH/100PA. Extra base hits per 100 plate appearances. Extra bases hits that can be

reasonably expected from a particular player if he comes to the plate 100 times.


RBI/100PA. Runs batted in per 100 plate appearances. The number of runs that a

particular player can be expected to drive in if he comes to the plate 100 times.


R/100PA. Runs scored per 100 plate appearances. The number of runs that a particular

player can be expected to score if he comes to the plate 100 times.


W/100PA. Walks per 100 plate appearances. The number of walks that a particular player

can be expected to score if he comes to the plate 100 times.


H/100PA. Hits per 100 plate appearances. The number of hits that a particular player

can be expected to accumulate if he comes to the plate 100 times.


OM. Outs Made. Every batter who comes to the plate is attempting to achieve a positive

outcome, but another way of looking at baseball is to say that  batters and baserunners 
should be doing everything possible to avoid making outs. The  context of a baseball game
is the 27 outs allotted to each team. Some players are  responsible for a greater percentage
of their team's outs than others. In DOSBall, this value is  the sum total of all outs for
which the player is responsible. It includes batting outs,  baserunning outs, and caught
stealing. Outs made figures into the calculation of runs created  per game. 

OM/HR. Outs made per homerun. The average number of outs that a player makes before 
hitting a homerun.  
OM/RB. Outs made per reaching base. The average number of outs that a player makes before
reaching base.  
XBH/PWR. Extra base hits as a percentage of APBA power rating. Players above 10 are generally
considered to be delivering "true-to-form" on a strong APBA power rating; anything above 20
is considered very solid. 
3BSB. Triples and stolen bases as a function of offensive performance. This stat simply measures
a player's speed impact on game play; a player who hits a lot of triples and steals a lot of bases
is going to have a 3BSB close to 1.0. If he has more than 1.0, the player's speed impact is at elite
levels and has a direct impact on winning more games for your team. Think of it as WHIP for baserunners,
but higher is better.  

BABIP. Batting Average for Balls in Play. The batting average for a player when he does not strike out.

OBP-AVG. On-Base Percentage minus Batting Average. Players who have .100 or more are considered excellent
at reaching base; a measure of a player's ability to find a way on base when they do not get a hit.  

RC/G. Runs created per game. Runs created is an accumulation stat; the more a player bats, the more runs
he creates (assuming he make some positive contribution). Converting runs created into runs created per
game provides an indication of how valuable this player is to have in the lineup.  RC/G is somewhat like 
ERA is for pitchers; it recasts the offensive contribution of the player in the context of a nine-inning 
(in this case, 27 out) game. To calculate RC/G, multiply RC by 27 and divide by the number of outs the
player is responsible for (OM), thus:

       RC/G = 27*RC/OM

One way to look at RC/G is to imagine a lineup with the same player batting in every spot.  A team made up
of nine 1992 model Barry Bonds, for example, would be expected to score 11.34 runs per game on average.
(Bonds had 147 runs created in 1992.)

SECA. Secondary Average. A measure of a player's offensive contributions that are not adequately reflected
by his batting average.  A player may have a relatively low batting average and still make a significant
contribution to his team's offense.  SECA reflects these contributions.  A Bill James creation.

       SECA = [D+(2*T)+(3*HR)+BB+SB-CS]/AB

That is, add the bases reached via extra base hits to walks and net stolen bases (stolen bases minus
caught stealing) and divide the sum by at bats.

Bigs: The 1993 combined major league secondary average was .257.  While SECA is roughly comparable
to batting average, the spread of SECA for players is broader than batting average.  League leading
SECA are on the order of .450, while many players have a SECA as low as .150.  (1993 SECA leaders:
Bonds-.629  Ricky Henderson-.545)

PWR-SP. Power-Speed Measurement. Bill James claims to have developed this stat in the early 1980s.  It
is a way of stating a player's combined ability to hit home runs and steal bases.  The formula is:

       Pw-Sp = (HR*SB*2)/(HR+SB)

It is so designed that if a player hits 30 home runs and steals 30 bases, his power-speed number will
be 30.0.  If he hits 20 homers and steals 40 bases, it will be 26.7.

Rickey Henderson posted a Pw-Sp number of 42.4 in 1986 when he hit 28 home runs and stole 87 bases.
Jose Canseco's 1988 performance of 42 HR and 40 SB produced a 41.0 Pw-Sp.  Willie Mays is the all-time
career leader with a 447.1 Pw-Sp for his career.  Through 1993, Rickey Henderson had accumulated a
366.4 career value.

wOBA. Weighted On-Base Average. A FanGraphs stat. Weighted On-Base Average (wOBA) is one of the most
important and popular catch-all offensive statistics. It was created by Tom Tango (and notably used 
in “The Book”) to measure a hitter’s overall offensive value, based on the relative values of each
distinct offensive event.

wOBA is based on a simple concept: Not all hits are created equal. Batting average assumes that they
are. On-base percentage does too, but does one better by including other ways of reaching base. Slugging
percentage weights hits, but not accurately (Is a double worth twice as much as a single? In short, no).
On-base plus slugging (OPS) does attempt to combine the different aspects of hitting into one metric,
but it assumes that one percentage point of SLG is the same as that of OBP. In reality, a handy estimate
is that OBP is around twice as valuable than SLG (the exact ratio is x1.8).

Weighted On-Base Average combines all the different aspects of hitting into one metric, weighting each
of them in proportion to their actual run value. While batting average, on-base percentage, and slugging
percentage fall short in accuracy and scope, wOBA measures and captures offensive value more accurately
and comprehensively. The wOBA formula for the 2012 season was:

wOBA = (0.691×uBB + 0.722×HBP + 0.884×1B + 1.257×2B + 1.593×3B +2.058×HR) / (AB + BB – IBB + SF + HBP)

wRAA. Weighted Runs Above Average. Measures the number of offensive runs a player contributes to their team
compared to the average player. How much offensive value did Evan Longoria contribute to his team in 
2009? With wRAA, we can answer that question: 28.3 runs above average. A wRAA of zero is league-average,
so a positive wRAA value denotes above-average performance and a negative wRAA denotes below-average
performance. This is also a counting statistic (like RBIs), so players accrue more (or fewer) runs as
they play. Calculating wRAA is simple if you have a player's wOBA value: subtract the league average
wOBA from your player's wOBA, divide by the wOBA scale coeeficient (1.26 for 2011), and multiply that
result by how many plate appearances the player received.

wRAA = ((wOBA - league wOBA) / wOBA scale) x PA

BF. Batters Faced. The total number of batters that a pitcher faces. This includes the times when batters
reach base, and when they do not. 

BF - S. Batters Faced as a Starting Pitcher. The number of batters that a pitcher has faced as a
starting pitcher.

BF - R. Batters Faced as a Relief Pitcher. The number of batters that a pitcher has faced as a
relief pitcher.

BF/9. Batters Faced Per 9 Innings. An average of the number of batters a pitcher has faced for every
nine innings he has pitched.  Calculated similarly to ERA, that is:

       [BF/9] = 9*BF/IP

In most instances of typical games, a team will send between 35 and 39 batters to the plate.  Thus,
an average pitcher will face between 35 and 39 batters per nine innings.  Less than 35 is a quality
pitcher.  More than 39 is a pitcher who has a tough time getting batters out. 
QS. Starts made divided by quality starts. The closer a pitcher is to 1.0, the more solid he is
as a starter.



 "The APBA Journal."  Howard Ahlskog, Editor and Publisher.

 Address: 65 Norwood, Greenfield, MA 01301. Monthly. $15.00 (1987)


 Boswell, Thomas.  How Life Imitates the World Series.

 New York: Penguin Books, 1983 (hardback, Doubleday, 1982).  ppb $5.95


 James, Bill. The Baseball Abstract.  New York: Ballantine Books,

 Annually 1982 to 1988.  $8.95 each


 Neft, David S. and Richard M. Cohen.  The Baseball Sports Encylopedia,

 1988 Edition.  New York: St. Martin's Press.  $15.95


 Project Scoresheet.  The Great American Baseball Stat Book.

 New York: Ballantine Books, 1987.  $12.95


 Siwoff, Seymour, and Steve Hirdt and Peter Hirdt.

 The Elias Baseball Analyst.  New York: Collier Books, 1987, 1988.  $12.95


 Thorn, John and Pete Palmer, with David Reuther.

 The Hidden Game of Baseball.  New York: Doubleday & Company, 1985. $10.95


   Unlock Your Imagination.


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